Recently, Open AI announced that one of their systems had proved one of the hardest maths problems in the world – the Navier-Stokes Millennium Problem, which comes with a million dollar reward. Naturally it has shaken the maths world, but there’s still a lot of confusion about what has actually been proved and how. To get to the bottom of it, we knew exactly who to ask: Chris Budd OBE, a Professor at the University of Bath and long-time Plus collaborator. Chris has worked on the Navier-Stokes equations and currently co-leads the Maths for Deep Learning research project and he tells us what it has been like on the mathematical/AI frontline.

This is a rapidly developing area – since recording this podcast it has been established that the Open AI result does not apply to the Navier-Stokes equations in full generality (i.e. without forcing). We are continuing to follow developments and will be sharing updates as more information is released. In fact, we will have a number of other episodes in this podcast series about AI and maths, so make sure you are following for more!

You might also like:

• An article on Navier-Stokes and AI
• A quick overview of the Navier-Stokes equations
• A collection of articles and podcasts on AI and mathematical proof
• All of our work with Chris on maths and deep learning

Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.

We are very lucky to be based at the Centre for Mathematical Sciences at the University of Cambridge. To start our latest podcast season we bring you a series of conversations with our mathematician colleagues, part of the podcast we produce for the Maths Faculty here.

In our first podcast we meet Richard Samworth, Professor of Statistical Science and Director of the Statistical Laboratory. We spoke to him in the run up to the International Congress of Mathematicians (ICM), one of the biggest dates in the mathematical calendar, where the most prestigious prizes in maths, including the Fields Medals, are awarded. Held every four years, the ICM features the world's leaders in the field and celebrates the diversity of today’s mathematics. Only mathematicians whose work is of the highest international standard are invited to speak at the week-long event, and Richard is one of the invited speakers at the ICM this July!

Richard's contributions to statistics have been recognised with numerous honours and awards. In 2025, he won two prestigious prizes in the space of 24 hours – the David Cox Medal for Statistics and the Guy Medal in Silver.

We talked to Richard to find out more about the work he will be speaking about at the ICM, how his field of statistics is simultaneously very theoretical and very applied, and what he most values about being part of the mathematical community here in Cambridge.

Find out more about:

• Richard's work
• Other Cambridge mathematicians invited to speak at the 2026 ICM
• The 2022 ICM
• The history of the ICM

Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.

We are continuing our conversations with mathematician colleagues at the University of Cambridge, part of the podcast we produce for the Maths Faculty here. Today we meet Julian Sahasrabudhe, Professor of Mathematics, and one of the invited speakers at the International Congress of Mathematicians (ICM) in July this year.

The ICM is one of the biggest events in the mathematics world and is the host of several prizes, including the prestigious Fields Medal. Only mathematicians at the very forefront of research are invited to speak, so we were very excited to learn more about Julian's work.

We spoke to him about his path into mathematics, from his childhood dreams to his early career as a drummer, before he finally settled on maths. Julian also gave us a brief introduction to his work in the field of combinatorics and how it offers partnerships with other areas of maths.

The podcast mentions Maryna Viazovska, who won a Fields Medal in 2022. Julian discusses the link between Ramsey theory and her work on sphere packing, as in the image below (courtesy Greg A L, CC BY-SA 3.0).

Find out more about:

• Julian's work and its connections to sphere packings
• Combinatorics
• Other Cambridge mathematicians invited to speak at the 2026 ICM
• The 2022 ICM

Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.